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Aims: Phosphorus (P) is an essential nutrient necessary for maintaining crop growth, however, it's often used inefficiently within agroecosystems, driving industry to find new ways to deliver P to crops sustainably. We aim to combine traditional soil and crop measurements with climate-driven mathematical models, to give insight into optimising the timing and placement of fertiliser applications. Methods: The whole plant crop model combines an above-ground leaf model with an existing spatially explicit below-ground root-soil model to estimate plant P uptake and above ground dry mass. We let P-dependent photosynthesis estimate carbon (C) mass, which in conjunction with temperature sets the root-growth-rate. Results: The addition of the leaf model achieved a better estimate of two sets of barley field trial data for plant P uptake, compared with just the root-soil model alone. Furthermore, discrete fertiliser placement increases plant P uptake by up to 10 % in comparison to incorporating fertiliser. Conclusions: By capturing essential plant processes we are able to accurately simulate P and C use and water and P movement during a cropping season. The powerful combination of mechanistic modelling and experimental data allows physiological processes to be quantified accurately and useful agricultural predictions for site specific locations to be made. [ABSTRACT FROM AUTHOR]

Aims: The readily available global rock phosphate (P) reserves may be depleted within the next 50-130 years warranting careful use of this finite resource. We develop a model that allows us to assess a range of P fertiliser and soil management strategies for Barley in order to find which one maximises plant P uptake under certain climate conditions. Methods: Our model describes the development of the P and water profiles within the soil. Current cultivation techniques such as ploughing and reduced till gradient are simulated along with fertiliser options to feed the top soil or the soil right below the seed. Results: Our model was able to fit data from two barley field trials, achieving a good fit at early growth stages but a poor fit at late growth stages, where the model underestimated plant P uptake. A well-mixed soil (inverted and 25 cm ploughing) is important for optimal plant P uptake and provides the best environment for the root system. Conclusions: The model is sensitive to the initial state of P and its distribution within the soil profile; experimental parameters which are sparsely measured. The combination of modelling and experimental data provides useful agricultural predictions for site specific locations. [ABSTRACT FROM AUTHOR]

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow. [ABSTRACT FROM AUTHOR]

At a time of increasing global demand for food, dwindling land and resources, and escalating pressures from climate change, the farming industry is undergoing financial strain, with a need to improve efficiency and crop yields. In order to improve efficiencies in farming, and in fertiliser usage in particular, understanding must be gained of the fertiliser-to-crop-yield pathway. We model one aspect of this pathway; the transport of nutrients within the vascular tissues of a crop plant from roots to leaves. We present a mathematical model of the transport of nutrients within the xylem vessels in response to the evapotranspiration of water. We determine seven different classes of flow, including positive unidirectional flow, which is optimal for nutrient transport from the roots to the leaves; and root multidirectional flow, which is similar to the hydraulic lift process observed in plants. We also investigate the effect of diffusion on nutrient transport and find that diffusion can be significant at the vessel termini especially if there is an axial efflux of nutrient, and at night when transpiration is minimal. Models such as these can then be coupled to whole-plant models to be used for optimisation of nutrient delivery scenarios. [ABSTRACT FROM AUTHOR]